Geodesic
Chain Condition and Fundamental Relation on $(\Delta,G)$-Sets Derived from $\Gamma$-semihypergroups
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 1, p. 21

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The aim of this research work is to define a new class of hyperstructure as a generalization of semigroups, semihypergroups and $\Gamma$-semihypergroups that we call $(\Delta,G)$-sets. Also, we define fundamental relation on $(\Delta,G)$-sets and prove some results in this respect. Then, we introduce the notions of quotient $(\Delta,G)$-sets by using a congruence relations. Finally, we introduce the concept of complete parts and Noetherian(Artinian) $(\Delta,G)$-sets.
Classification : 20N15
Keywords: $\Gamma$-semihypergroup, left(right) $(\Delta;G)$-set, twist product, flat $\Gamma$-semihypergroup, absolutely flat $\Gamma$-semihypergroup 
S. Ostadhadi-Dehkordi. Chain Condition and Fundamental Relation on $(\Delta,G)$-Sets Derived from $\Gamma$-semihypergroups. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 1, p. 21 . http://geodesic.mathdoc.fr/item/KJM_2021_45_1_a1/
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     title = {Chain {Condition} and {Fundamental} {Relation} on $(\Delta,G)${-Sets} {Derived} from $\Gamma$-semihypergroups},
     journal = {Kragujevac Journal of Mathematics},
     pages = {21 },
     year = {2021},
     volume = {45},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2021_45_1_a1/}
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